To solve the problem of determining how much money will be in an account after 29 years with a principal of [tex]$4400 and an annual interest rate of 8.25%, we'll use the compound interest formula. The compound interest formula is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of times that interest is compounded per year.
- \(t\) is the time the money is invested for in years.
Given:
- \(P = 4400\) dollars
- \(r = 0.0825\) (since 8.25% converted to decimal form is 0.0825)
- \(n = 1\) (assuming the interest is compounded annually)
- \(t = 29\) years
Substitute these values into the formula:
\[ A = 4400 \left(1 + \frac{0.0825}{1}\right)^{1 \cdot 29} \]
\[ A = 4400 \left(1 + 0.0825\right)^{29} \]
\[ A = 4400 \left(1.0825\right)^{29} \]
Through computation:
\[ A = 4400 \times 9.96343853017 \] (exact value from calculations)
\[ A \approx 43839.129531474 \]
Finally, rounding this amount to the nearest cent, we get:
\[ A \approx 43839.13 \]
Thus, after 29 years, the amount in the account will be approximately $[/tex]43,839.13.
